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1092

Appendix VI.

4 I*

4.  Draw parallel lines in the vector figure, shewn dotted, and
obtain the pole O2 for a polygon passing through A and B only.

5.  To pass through A, B and c, adopt the rotation method,
where A and B will be turning points, and the line e e a line of
turning points.

6.  Draw 02 OF || AB : also produce jk to el and join el to c;
then draw 5 0P || / mt and the final pole 0F is found.

7.  The link polygon through ABC may now be completed by
rotation, or by reference to the vector figure 50Fo.

Applications of the foregoing problem. Let us first consider
the conditions as to the distribution of pressure between the
voussoirs or blocks of a stone arch. In Fig. 965, v v are a pair
of voussoirs, held together by mortar that may be sufficient to

i"

t'j
I I

tl

FAq. 965.

on, cu

resist sliding, but which is not to be subjected to any tension
whatever. So long as the direction of pressure is in the centre
of the voussoir we feel sure that the conditions are safe; but we
now require to know how far the line of pressure may deviate
above or below the centre line without causing the joint to open.
Let the pressure be exerted by the force P, whose distance down-
ward from the centre is xh> We may place two balanced forces
at the centre line, each equal to P, without altering the con-
ditions, and we now have two actions to consider: (i) a mo-
ment P x xh tending to open the joint at a a, and (2) a pressure P
at the centre line, tending to close the joint If these two actions
balance, the joint will have neither pressure or tension, but will
remain closed.